Question

does D,E and F being pairwise independent imply that D,E and F are mutually independent? (Foget this question)

Answer #1

If P(E) = 0.32 and P(F) = 0.25:
a.) Find P (E or F) if E and F are mutually exclusive.
b.) Find P (E and F) if E and F are independent.

When does a supply-side gap directly imply a demand-side gap? And
when are they independent?

Show that if E and F are independent, then E^C and F^C are
independent. Please explain each step thoroughly. Thank you in
advance!

Uncorrelated and Gaussian does not imply independent unless
jointly Gaussian. Let X ∼N(0,1) and Y = WX, where p(W = −1) = p(W =
1) = 0 .5. It is clear that X and Y are not independent, since Y is
a function of X. a. Show Y ∼N(0,1). b. Show cov[X,Y ]=0. Thus X and
Y are uncorrelated but dependent, even though they are Gaussian.
Hint: use the deﬁnition of covariance cov[X,Y]=E [XY] −E [X] E [Y ]
and...

4. What does it mean to say an investment is independent and not
mutually exclusive?

List at least two ways that higher real GDP/person does imply
greater economic well-being

Suppose that events E and F are independent, P(E) =0.3 and P(F )
=0.6, P( E and F)=0.2 What is the P( E or F ) ?

What is P(C|D), given P(D|C) = 0.1, P(C) = 0.2, P(D|E) = 0.25,
P(E) = 0.5, P(D|F) =0.75, and P(F) = 0.5, where E and F are
mutually exclusive and exhaustive events(either E happens or F
happens, and one of the two must happen)

E and F be any experiments with their probabilities as p(E) =
0.73 and P(F) = 0.58
1. the two given experiments are mutually exclusive, find p(E or
F)
2. If the two given experiments are not mutually exclusive and
p(E&F)= 0.45 , find p(E U F).
Please provide with all steps TIA

Does P(A∩B|C)=P(A|C)P(B|C) imply that A and B are independent?
Assume P(C)>0, so that the conditional probabilities are
defined.
- yes
- no
Please explain the answer

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